一类强部分平衡设计的构造

利用强部分平衡设计可以构造最佳认证码和密钥预分配方案,本文提出了一种强 部分平衡设计的构造方法,并给出了利用这种方法得到的一些结果.     

二面体群上构作的结合方案

本文研究了二面体群的元素的等价划分问题。利用群在集合上的作用,在二面体群上构造了一类新的结合方案,并且计算了这类结合方案的所有参数。进一步,得到了一类强正则图。所得到的结果丰富了结合方案理论。     

二面体群上构作的结合方案（英文）

本文研究了二面体群的元素的等价划分问题.利用群在集合上的作用,在二面体群上构造了一类新的结合方案,并且计算了这类结合方案的所有参数.进一步,得到了一类强正则图.所得到的结果丰富了结合方案理论.     

完美门限方案的组合构造

部分平衡t-设计t-(v; b;w; 1; 0) (X;A) 称为可划分的, 如果它同时也是一个部分平衡(t-1)-设计(t -1)-(v; b;w; λ_t-1; 0) 并且可将区组集A划分为A₁;…;A_λt-1; 使得每个(X;A_i) (1≤i≤λ_t-1)是一个部分平衡(t-1)-设计(t-1)-(v; b/λ_t-1;w; 1; 0). 本文证明可划分部分平衡t-设计PPBD t-(v; b;w;λ_t-1; 1; 0) 的存在性蕴含着完美(t;w; v;λ_t-1)-门限方案的存在性; 而且在某些情况下, 最优可划分部分平衡t-设计OPPBD(t;w; v) 的存在性等价于最优(t;w; v)-门限方案的存在性. 由此我们得到了最优(t;w; v)-门限方案的一些新的无穷类.     

方程(x·)(t)=-x[t-π/3√3]-x[t-2π/3√3]周期解的部分表达式

文[1]给出了一类具两个滞量的方程存在周期解的充分条件,但并没有给出周期解的表达式.本文给出了方程(x·)(t)=-x[t-π/3√3]-x[t-2π/3√3]周期解的部分表达式.     

方程x（t）= —x[t—π／3—√3]—x[t—2π／3√3]周期解的部分表达式

文[1]给出了一类具两个滞量的方程存在周期解的充分条件，但并没有给出周期解的表达式，本文给出了方程x(t)= -x[t-π/3-√3]-x[t-2π/3√3]周期解的部分表达式。     

方程(t)=-x〔t-π/(33~(1/2))〕-x〔t-2π/(33~(1/2))〕周期解的部分表达式

]文 [1 ]给出了一类具两个滞量的方程存在周期解的充分条件 ,但并没有给出周期解的表达式 .本文给出了方程 x( t) =-x t-π3 3-x t-2π3 3周期解的部分表达式 .     

关于每区组包含两个处理的一类部分平衡设计

1.引言 作为一对比较的一类试验设计,Clatworthy研究每个区组包含两个处理的两个结合类部分平衡不完备区组设计;对k=2和2≤r≤10,利用Connor-Clatworthy关于这类设计存在的必要条件,枚举了设计的参数组,并除四个例外,给出了设计的解(构造)。但是,Clatworthy的枚举并不穷尽。我们在研究结合方案的存在问题中发现文献[2]的枚举有一个脱漏,这个脱漏的和其中的四个例外的参数组如下:     

一种构造可积Hamilton系统的新方法

建议了一种新的构造可积Hamilton系统的方法。对于给定的Poisson流形,本文利用Dirac-Poisson结构构造其上的新Poisson括号[1],进而获得了新的可积Hamilton系统。构造的Poisson括号一般是非线的,并且这种方法也不同于通常的方法[2～4]。本文还给出了两个实例。     

一类新的广义零差分平衡函数及其应用

2008-2009年,丁存生在构造最佳常组合码与优化及完善差分系统中首次引入了零差分平衡(简称ZDB)函数的概念,据此学者们构造出了最佳组成权重码和最优跳频序列.作者将零差分平衡函数的定义推广到一般的广义零差分平衡函数,并利用2分圆陪集构造了一类广义零差分平衡函数,由此构造出一类新的常组合码和差分系统.     

A problem of combinatorial designs related to authentication codes

The strong partially balanced t-designs can be used to construct authentication codes, whose probabilities P_r of successful deception in an optimum spoofing attack of order r for r = 0, 1, …, t − 1, achieve their information-theoretic lower bounds. In this paper a new family of strong partially balanced t-designs are constructed by means of rational normal curves over finite fields. Thus based on this new partially balanced t-designs a new class of authentication codes is obtained. © 1998 John Wiley & Sons, Inc. J Combin Designs 6: 417–429, 1998     

Trading Signed Designs and Some New 4-(12, 5, 4) Designs

Variations of the trade-off method exist in the literature of design theory and have been utilized by some authors to produce some t-designs with or without repeated blocks. In this paper we explore a new version of this algorithmic method (i) to produce 20 nonisomorphic and rigid 4-(12,5,4) designs, (ii) to study the spectrum of support sizes of 4-(12,5,4) designs. Along these, we also present a new design invariant for testing isomorphism among designs and a new way of representing t-designs.     

New Combinatorial Bounds for Authentication Codes and Key Predistribution Schemes

This paper provides new combinatorial bounds and characterizations of authentication codes (A-codes) and key predistribution schemes (KPS). We first prove a new lower bound on the number of keys in an A-code without secrecy, which can be thought of as a generalization of the classical Rao bound for orthogonal arrays. We also prove a new lower bound on the number of keys in a general A-code, which is based on the Petrenjuk, Ray-Chaudhuri and Wilson bound for t-designs. We also present new lower bounds on the size of keys and the amount of users' secret information in KPS, the latter of which is accomplished by showing that a certain A-code is hiding inside any KPS.     

A class of pbib-designs obtained from projective geometries

In this paper, a new class of partially balanced incomplete block designs is constructed over an association scheme obtained from a finite projective geometry. Further, a general method for deriving a balanced incomplete block design from another one is given.     

Butson Hadamard matrices with partially cyclic core

In this paper, we introduce a class of generalized Hadamard matrices, called a Butson Hadamard matrix with partially cyclic core. Then a new construction method for Butson Hadamard matrices with partially cyclic core is proposed. The proposed matrices are constructed from the optimal balanced low-correlation zone(LCZ) sequence set which has correlation value ?1 within LCZ.     

强正则图的一些性质

文[3]给出了强正则图的概念及有关性质,本文在此基地上利用图的谱性质,得到了强正则图的又一些性质。     

Partially balanced incomplete block designs from weakly divisible nearrings

In [[6] Riv. Mat. Univ. Parma 11 (2) (1970) 79-96] Ferrero demonstrates a connection between a restricted class of planar nearrings and balanced incomplete block designs. In this paper, bearing in mind the links between planar nearrings and weakly divisible nearrings (wd-nearrings), first we show the construction of a family of partially balanced incomplete block designs from a special class of wd-nearrings; consequently, we are able to give some formulas for calculating the design parameters.     

Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces

In this paper, we prove a strong convergence theorem by the hybrid method for a family of nonexpansive mappings which generalizes Nakajo and Takahashi's theorems [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379], simultaneously. Furthermore, we obtain another strong convergence theorem for the family of nonexpansive mappings by a hybrid method which is different from Nakajo and Takahashi. Using this theorem, we get some new results for a single nonexpansive mapping or a family of nonexpansive mappings in a Hilbert space.